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Manipulation and sorting of particles utilizing microfluidic phenomena have been a hot spot in recent years. Here, we present numerical investigations on particle trapping techniques by using intrinsic hydrodynamic effects in an expansion-contraction microfluidic device. One emphasis is on the underlying fluid dynamical mechanisms causing cross-streamlines migration of the particles in shear and vortical flows. The results show us that the expansion-contraction geometric structure is beneficial to particle trapping according to its size. Particle Reynolds number and aspect ratio of the channel will influence the trapping efficiency greatly because the force balance between inertial lift and vortex drag forces is the intrinsic reason. Especially, obvious inline particles contribution presented when the particle Reynolds number being unit. In addition, we selected three particle sizes (2, 7, and 15

Microfluidics has greatly interested many researchers in recent years, and has been widely used in the areas of nanomaterials preparation, pharmaceutical analysis, protein engineering, and so on [

Passive methods used to trapping particles by exerting hydrodynamic force are arising in microfluidic devices. The main approaches are the cross-stream migration of suspended particles in confined flows and microvortical flow. The microvortex generated in sudden expansion is of great importance for particle manipulation. Researchers have gained some beneficial research results [

In the present research, microvortex in the expansion-contraction microchannel is numerically studied in order to understand the particle migration mechanism. The particles distribution and equilibrium position will vary with the change of inlet flow rate and geometry dimensions. Moreover, the research object is also to gain an insight into what condition being beneficial to the particle trapping efficiency for varying particle sizes and to supply the design foundations of such a microfluidic device.

The microdevice under investigation is presented in Figure

Geometric model of the expansion-contraction microfluidic device.

The settings of carried fluid properties: the viscosity, density, specific heat, and thermal conductivity of continuous phase are 1.003 g/m·s, 0.9982 g/cm^{3}, 4180 J/kg·K, and 0.6 W/m·K, respectively. Density and specific heat of polystyrene microspheres are 1.055 g/cm^{3} and 1300 J/kg·K.

The numerical model includes the continuity equation, Navier-Stokes equation which is still valid in current microchannel flow, and continuity equation for volume fraction

The particle continuity is derived from Buongiorno [

There is still a lack of accurate theoretical models for the prediction of the viscosity the fluid containing particles. Normally, empirical laws [

In order to verify the availability of the numerical model, we simulated numerically the flow with particles in a circular capillary. The particles distributions are shown in Figure

The contour lines of particle concentration in varying position of capillary. (a) 500

When particles are suspended in the carried fluid, the particle behavior is affected by the inertial and viscous forces occurring in the interaction with fluid. According to a number of theoretical analyses, the inertial migration phenomenon can be explained by a shear-gradient-induced lift force that causes particles to migrate away from the axis of pipe and a wall-effect-induced lift force that repels particles away from a pipe wall [

The contour line of particle concentration in varying aspect ratio (AR): (a)

The channel geometry of multiorifices pattern (expansion-contraction structure) was designed so as to transform the particle distribution in a cross section of a straight channel and subsequently concentrate particles close to both side walls of channel. The mechanism of particle enrichment is based on the vortex flow due to the suddenly expansion channel, as shown in Figure

Microvortex structure and particle movement in an orifice.

The channel geometry influences the particle trapping efficiency obviously. The main influence factors are aspect ratio, orifice number, and orifice structure. Figure

The contour line of particle concentration in varying position of our device: (a) position P0, (b) position P1, (c) position P2, (d) position P3, and (e) position P4.

Trapping efficiency comparison between two kinds of orifices.

Equation (

Particle contribution in various flow rates (with particle size being 7

Particle size is another important factor to influence particle trapping efficiency. We simulated 3 sizes of particles 2, 7, and 15 ^{3}/

Trapping efficiency comparison of three particle sizes.

After numerical simulations being carried out for various particle sizes under various flow rates in various orifices structures, the following conclusions can be drawn.

multiorifices structure is beneficial to particle trapping.

Aspect ratio of square channel influences the particle distribution greatly. When aspect ratio is bigger than 3, particle distribution appears to be two-lines structure, and loop line structure for less than 2 aspect ratios.

Particle Reynolds number is of great importance to particle trapping. When

The author declares that there is no conflict of interests regarding the publication of this paper.

The author acknowledges the support from the Natural Science Foundation of Zhejiang Province China (LY12A02007).